should I attempt to do this with or without internet connection?
With.
We should proceed with general antimalware scan which can take quite a long time so please be patient.
Download
Virus Removal Tool (VRT) from
Here to your desktop
(You have to enter your e-mail address and click on
Submit Form button. Please download latest English version of this tool)
Run the programme you have just downloaded to your desktop (it will be randomly named )
First we will run a virus scan Click the cog in the upper right

Select down to and including your main drive, once done select the Automatic scan tab and press
Start Scan (Please be patient as this scan can take a few hours)

Allow VRT to delete all infections found
Once it has finished select report tab (last tab)
Select
Detected threads report from the left and press
Save button
Save it to your desktop and attach to your next post
Now the AnalysisRerun VRT and select the
Manual Disinfection tab and press
Start Gathering System Information 
On completion click the link to locate the zip file to upload and attach to your next post